Computationally-assisted existence proofs in differential geometry
Speaker: Timothy Buttsworth
Affiliation: University of New South Wales
Abstract
In this talk, I will outline a general two-step approach that has the potential to be very useful in the construction of many ad hoc examples of special solutions of geometric PDEs. The first step is to obtain a (verifiably) highly-accurate approximate solution metric using numerical techniques, and the second step is to then use perturbative techniques to prove existence of a true solution near the approximate solution. I will report on recent work I have done with Liam Hodgkinson (Melbourne) which successfully uses this approach to prove existence of a new O(3)×O(10)-invariant Einstein metric on S^{12}. I will then go on to discuss other possible geometric applications.
About Pure mathematics seminars
We present regular seminars on a range of pure mathematics interests. Students, staff and visitors to UQ are welcome to attend, and to suggest speakers and topics.
Seminars are usually held on Tuesdays from 2 to 3pm.
Talks comprise 45 minutes of speaking time plus five minutes for questions and discussion.
Information for speakers
Researchers in all pure mathematics fields attend our seminars, so please aim your presentation at a general mathematical audience.
Contact us
To volunteer to talk or to suggest a speaker, email Ole Warnaar or Yang Zhang.
Venue
Room: 304